Michael Mullen <MEMullen@AOL.COM> wrote:

> Having some experience with precision instruments with floating point
> displays, I point out that I have never, in fact, found it necessary
> to actually do the calculations in floating point. I usually scale
> until I can do a fixed point operation, or operate with a scale
> factor.

Thanks for your reply to my query, Michael. My original posting
described a situation where fixed point calculations were not
suitable because the translation equations (and therefore the numeric
ranges) weren't known in advance. I'm working on a project at the
moment where user-replaceable sensors are plugged into a base unit;
each sensor having a 40-byte EEPROM (Dallas 24A30) containing the
sensor name (ie, LCD text string) and calibration constants, etc. The
main controller is not a PIC, but only because of the lack of
floating point support in the programming tools.

> In contrast, the constants given in Doug Manzer's tangent calculation
> are 9 decimal digits. If this were used to measure angles in a
> navigation system, one could measure one's longitude anywhere on the
> earth to to a precision of less than 2 inches. For most problems,
> this level of precision is overkill.

Agreed, although some guard digits are necessary. A 12-bit a/d
converter will return a result in the range 0 to 4095, ie. 4 decimal
digits so perhaps 5 or 6 digit precision would be reasonable in
calculations.

> I don't mean to be dogmatic; there _ARE_ valid reasons for FP and
> high precision operations. However, I would suggest strongly that, if
> you really need such things, you might consider a more powerful
> processor (or, more accurately, one with more powerful tools).
                                  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This is my whole point; there are compilers with the float data type
for the HC11, which has roughly the same computing power as the
higher-end PIC's so the problem with with the tools. Since this IS
a PIC forum I was hoping to find a PIC-based solution.

I can see three main phases in a f/p computation:

1.a Convert the acquired value (typically binary integer) to f/p in
whatever radix is used internally

1.b It may also be necessary to accept input in decimal format from
the user (eg. for calibration constants) which need to be translated
into f/p format.

2. Perform the f/p operations

3. Convert the result to readable form in decimal format


AND575 in Microchip's _Embedded Control Handbook_ provides only
partial solutions for these operations.

Phase 1.a at least is covered with an integer to float conversion.

Relevant to Phase 1.b, it includes a floating point to binary
conversion algorithm for which the first step is...

  z = ln A / ln 2

...however, the author doesn't include an ln() function in his
math library.

For Phase 2, AN575 covers only the 4 basic math functions with
no mention of transcendental functions.

Phase 3 is also awkward, as the library functions produce results in
Microchip's modified IEEE754 format. There is a float to integer
conversion, but only with a limited range. I would like to see an
equivalent to Borland's fcvt(), described in their _C++ Library
Reference_ as follows (with capitals in place of italics):

-----------------------------------------------------
Function  Converts a floating-point number to a string.

Syntax    #include <stdlib.h>
          char *fcvt(double VALUE,int NDIG,int*DEC,int *SIGN) ;

Remarks   fcvt converts VALUE to null-terminated string digits,
          starting with the leftmost significant digit, with NDIG
          digits to the right of the decimal point. fcvt then returns
          a pointer to the string. The position of the decimal point
          relative to the beginning of the string is stored indirectly
          through DEC (a negative value for DEC means to the left of
          the returned digits). There is no decimal point in the string
          itself. If the sign of value is negative, the word pointed
          to by SIGN is nonzero; othersie, it is 0.

          The correct digit has been rounded for the number of digits
          to the right of the decimal point specified by NDIG.

Ret  val  The return value of fcvt points to static data whose content
          is overwritten by each call to fcvt and ecvt.

See also  ecvt, gcvt, sprintf
-----------------------------------------------------

An ascii string with sign and exponent information could be used to
derive the message string for the readout, typically a 7-segment
display with format 8.8.8.8 or an LCD.

Regards, Doug Manzer

ps. thanks to everyone who emailed help and suggestions; I will
reply shortly.